- 2-1 Manipulating Rightmost Bits
- 2-2 Addition Combined with Logical Operations
- 2-3 Inequalities among Logical and Arithmetic Expressions
- 2-4 Absolute Value Function
- 2-5 Average of Two Integers
- 2-6 Sign Extension
- 2-7 Shift Right Signed from Unsigned
- 2-8 Sign Function
- 2-9 Three-Valued Compare Function
- 2-10 Transfer of Sign Function
- 2-11 Decoding a "Zero Means 2 **n" Field
- 2-12 Comparison Predicates
- 2-13 Overflow Detection
- 2-14 Condition Code Result of Add, Subtract, and Multiply
- 2-15 Rotate Shifts
- 2-16 Double-Length Add/Subtract
- 2-17 Double-Length Shifts
- 2-18 Multibyte Add, Subtract, Absolute Value
- 2-19 Doz, Max, Min
- 2-20 Exchanging Registers
- 2-21 Alternating among Two or More Values
- 2-22 A Boolean Decomposition Formula
- 2-23 Implementing Instructions for All 16 Binary Boolean Operations
This chapter is from the book
This chapter is from the book
This chapter is from the book
2–9 Three-Valued Compare Function
The three-valued compare function, a slight generalization of the sign function, is defined by
There are both signed and unsigned versions, and unless otherwise specified, this section applies to both.
Comparison predicate instructions permit a three-instruction solution, an obvious generalization of Equations in (4):
A solution for unsigned integers on PowerPC is shown below [CWG]. On this machine, “carry” is “not borrow.”
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If limited to the instructions of the basic RISC, there does not seem to be any particularly good way to compute this function. The comparison predicates x < y, x ≤ y, and so on, require about five instructions (see Section 2–12), leading to a solution in about 12 instructions (using a small amount of commonality in computing x < y and x > y). On the basic RISC it’s probably preferable to use compares and branches (six instructions executed worst case if compares can be commoned).